Question

solve for x in the triangle. round your answer to the nearest tenth. x =

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 20^{\circ}\), the opposite side is \(x\), and the adjacent side is \(15\). So, \(\tan(20^{\circ})=\frac{x}{15}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\tan(20^{\circ})=\frac{x}{15}\) by \(15\). We get \(x = 15\times\tan(20^{\circ})\).
Since \(\tan(20^{\circ})\approx0.364\), then \(x=15\times0.364 = 5.46\approx5.5\).

Answer:

\(x = 5.5\)